functions{
  real pald2(real mu, real p){
    real prob;
    if (mu <0){
      prob = p*exp((mu)*(1-p));
    } else {
      prob = 1-(1-p)*exp(-(mu)*(p));
    }
    return(prob);
}
}

data {
  int N; 
  int D; 
  vector<lower=-1,upper=1>[N] Y; 
  matrix[N,D] X; 
  real offset;
}


parameters {
  vector[D] beta;
  real alpha; 
}


model{
  real lik;
  alpha ~ normal(0,10);
  beta ~ normal(0,10);

  for (i in 1:N){
    if (Y[i] == 1){
      lik = pald2((alpha + dot_product(X[i,],beta)),0.5) + offset;  
    }
    if (Y[i] == 0){
      lik = 1 - pald2((alpha + dot_product(X[i,],beta)),0.5) + offset;  
    }

    target += log(lik);
  }
}



